I have the Mirena and have had zero issues with it. Since I decided that was what I wanted after my 3rd daughter was born, the doctor preferred to insert it at my 5-week post-partum check-up. If we'd waited, it would still have to have been during or at the end of a period (you need to be dilated at last 2 cm).
It's much more painful and uncomfortable for women who have never had children because they don't dilate enough during their periods yet.
A small percentage of women feel moderate to severe discomfort and pain during insertion, but most feel mild discomfort, nothing that a few Advil can't take care of.
You would likely get some mild cramping similar to very mild contractions, because your uterus would be saying, "Hey, that doesn't belong there, let's eject it." You might have very, very light spotting. A very few women have enough bleeding that they have to have the device removed.
I chose Mirena because it's VERY low dosage of hormone, and is not enough to go throughout your entire bloodstream. It's not even enough to cause acne because there's just not enough hormone in it unless you're super-sensitive to any/all hormone therapies. The fact is that the Pill can be used to treat acne, but the IUD can't even though it has progesterone in it because there's simply not enough.
There's also a chance that while your periods will get lighter, they could also stop until the IUD is removed. I think I get my period (lightly) once a year since I had it inserted back in March 2005.
I personally couldn't choose the copper or any other of the metallic ones because I have a contact skin allergy to copper and nickel. It would be a huge mistake for me to use them. Mirena is lightweight and it's plastic, so it's completely hypo-allergenic. I've actually lost weight on it, compared to gaining a lot of weight from the Pill because again, it has far less hormone than the Pill does.
Mirena does cost more (average is around $700-800 for hardware + procedure), and it might not be covered by your insurance. What you want to do in regard to worry about an IUD puncturing your uterus is to check your OB's track record for the procedure.